Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
514 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #23762082 | C2 | semidirect |
| 5. #23762080 | C2 | semidirect |
| 6. #23761303 | C2 | semidirect |
| 7. C79×#1303 | C2 | semidirect |
| 177. #1303 | D79 | semidirect |
| 178. C79 | #9399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772440 | 2 |
| #23768569 | 2 |
| #23763389 | 2 |
| #23762082 | 2 |
| #23762080 | 2 |
| #23761303 | 2 |
| C79×#1303 | 2 |
| #9399 | 79 |